C-Γ-hyperideal Theory in Ordered Γ-semihypergroups


  • Bijan Davvaz Department of Mathematics, Yazd University, Yazd
  • Saber Omidi Department of Mathematics, Yazd University, Yazd




C-𝛤-hyperideal, 𝛤-hyperideal, ordered 𝛤-semihypergroup, regular, semihypergroup


Our purpose in this article is to characterize the properties of C-Γ-hyperideals in ordered Γ-semihypergroups. As an application of the results of this paper, the corresponding results of ordered semihypergroups can also be obtained by moderate modification.


Sen, M.K. & Saha, N.K., On "-semigroup I, Bull. Calcutta Math. Soc., 78, pp. 180-186, 1986.

Sen, M.K. & Seth, A., On Po-"-semigroups, Bull. Calcutta Math. Soc., 85, pp. 445-450, 1993.

Chinram, R. & Tinpun, K., A Note on Minimal Bi-Ideals in Ordered "-semigroups, International Math. Forum., 4(1), pp. 1-5, 2009.

Dutta, T.K. & Adhikari, N.C., On Prime Radical of "-semigroup, Bull. Calcutta Math. Soc., 86(5), pp. 437-444, 1994.

Hila, K., On Quasi-Prime, Weakly Quasi-Prime Left Ideals in Ordered "-semigroups, Math. Slovaca, 60(2), pp. 195-212, 2010.

Iampan, A., Characterizing Ordered Bi-Ideals in Ordered "-semigroups, Iran. J. Math. Sci. Inform., 4(1), pp. 17-25, 2009.

Kehayopulu, N., On Ordered "-semigroups, Sci. Math. Japonicae., 71(2), pp. 179-185, 2010.

Kwon, Y.I., The Filters of The Ordered "-semigroups, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 4, pp. 131-135, 1997.

Tang, J. & Xie, X.Y., On a-Maximal Ideals and C-ideals of Ordered "-semigroups, Thai J. Math., 11(1), pp. 189-198, 2013.

Fabrici, I., Semigroups Containing Covered One-sided Ideals, Math. Slovaca, 31(3), pp. 225-231, 1981.

Fabrici, I., Semigroups Containing Covered Two-sided Ideals, Math. Slovaca, 34(4), pp. 355-363, 1984.

Fabrici, I. & Macko, T., On Bases and Maximal Ideals in Semigroups, Math. Slovaca, 31(2), pp. 115-120, 1981.

Xie, X.Y., On Po-Semigroups Containing No Maximal Ideals, Southeast Asian Bull. Math., 20(4), pp. 31-36, 1996.

Changphas, T. & Summaprab, P., Ordered Semigroups Containing Covered Ideals, Comm. Algebra., 44, pp. 4104-4113, 2016.

Marty, F., Sur Une Generalization De La Notion De Groupe, 8^iem Congres Math. Scandinaves, Stockholm, Sweden, pp. 45-49, 1934.

Corsini, P., Prolegomena of Hypergroup Theory, 2nd ed., Aviani Editore, Italy, 1993.

Corsini, P. & Leoreanu, V., Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, 2003.

Davvaz, B. & Leoreanu-Fotea, V., Hyperring Theory and Applications, International Academic Press, Palm Harbor, USA, 2007.

Vougiouklis, T., Hyperstructures and Their Representations, Hadronic Press Inc., Florida, 1994.

Ameri, R. & Hoskova, S., Fuzzy Continuous Polygroups, APLIMAT 2016-15th Conference on Applied Mathematics, Proceedings, Slovak University of Technology in Bratislava, pp. 13-19, 2016.

Ameri, R., Amiri-Bideshki, M., Saeid, A.B. & Hoskova, S., Prime filters of hyperlattices, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 24(2), pp. 15-26, 2016.

Chvalina, J. & Hoskova, S., On Certain Proximities and Preorderings on The Transposition Hypergroups of Linear First-Order Partial Differential Operators, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 22(1), pp. 85-103, 2014.

Heidari, D. & Davvaz, B., On Ordered Hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 73(2), pp. 85-96, 2011.

Anvariyeh, S.M., Mirvakili, S. & Davvaz, B., On "- hyperideals in "-Semihypergroups, Carpathian J. Math., 26(1), pp. 11-23, 2010.

Anvariyeh, S.M., Mirvakili, S. & Davvaz, B., Pawlak's Approximations in "-semihypergroups, Comput. Math. Appl., 60(1), pp. 45-53, 2010.

Heidari, D., Dehkordi, S.O. & Davvaz, B., "-semihypergroups and their Properties, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 72(1), pp. 197-210, 2010.

Davvaz, B. & Leoreanu-Fotea, V., Structures of Fuzzy "-hyperideals of "-semihypergroups, J. Multiple-Valued Logic and Soft Computing, 19(5-6), pp. 519-535, 2012.

Hila, K., Davvaz, B. & Dine, J., Study on The Structure of "-semihypergroups, Commun. Algebra, 40(8), pp. 2932-2948, 2012.

Yaqoob, N. & Aslam, M., On Rough Quasi-"-Hyperideals in "-semihypergroups, Afr. Mat., 26(3-4), pp. 303-315, 2015.

Davvaz, B. & Omidi, S., Basic Notions and Properties of Ordered Semihyperrings, Categ. General Alg. Structures Appl., 4(1), pp. 43-62, 2016.

Chvalina, J., Commutative Hypergroups in The Sence of Marty and Ordered Sets, Proceedings of the Summer School in General Algebra and Ordered Sets, Olomouck, pp. 19-30, 1994.

Davvaz, B., Corsini, P. & Changphas, T., Relationship Between Ordered Semihypergroups and Ordered Semigroups by Using Pseudoorder, European J. Combin., 44(PB), pp. 208-217, 2015.

Gu, Z. & Tang, X., Ordered Regular Equivalence Relations on Ordered Semihypergroups, J. Algebra, 450, pp. 384-397, 2016.

Tang, J., Davvaz, B. & Luo, Y.F., Hyperfilters and Fuzzy Hyperfilters of Ordered Semihypergroups, J. Intell. Fuzzy Systems, 29(1), pp. 75-84, 2015.

Kondo, M. & Lekkoksung, N., On Intra-Regular Ordered "-semihypergroups, Int. Journal of Math. Analysis, 7(28), pp. 1379-1386, 2013.